Distance between parallel lines

Hello. In this lesson, I’ll derive the expression for finding out the distance between two parallel lines.

It’s quite straightforward – the distance between two parallel lines is the difference between the distances of the lines from a point.

This is what I’m talking about..

Let the equations of the lines be ax+by+c1=0 and ax+by+c2=0. Let P(x1, y1) be any point. The required distance d will be PA – PB.

(Note that the coefficients of x and y in both the lines will be correspondingly equal or proportional, because they are parallel. In case they’re not equal, you should transform the equation accordingly. I’ll discuss this during examples.)